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Page 1: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Magnetic Circuit

SUBHASH PATEL

Electronics & Communication

Year 2010

Page 2: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Outline

1 Magnetomotive Force (MMF)

2 Reluctance

Page 3: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Outline

1 Magnetomotive Force (MMF)

2 Reluctance

Page 4: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Magnetomotive Force (MMF)

The current flowing in the electrical circuit due to the existence of electromotiveforce(emf) across the circuit

To drive magnetic flux through magnetic circuit, a magneto motive force (mmf)is necessary.

Magnetomotive force can be produced when current flows in a coil of one ormore turns.

The magnitude of mmf is directly proportional to the current I and number ofturns of the coil N,mmf = NI

If the magnetic circuit of magnetic material is homogeneous and of uniformcross sectional area, the magnetomotive force per meter length of the magneticcircuit (path of magnetic flux) is called the magnetic field strength (H).

H =mmf

l

Page 5: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Magnetomotive Force (MMF)

The current flowing in the electrical circuit due to the existence of electromotiveforce(emf) across the circuit

To drive magnetic flux through magnetic circuit, a magneto motive force (mmf)is necessary.

Magnetomotive force can be produced when current flows in a coil of one ormore turns.

The magnitude of mmf is directly proportional to the current I and number ofturns of the coil N,mmf = NI

If the magnetic circuit of magnetic material is homogeneous and of uniformcross sectional area, the magnetomotive force per meter length of the magneticcircuit (path of magnetic flux) is called the magnetic field strength (H).

H =mmf

l

Page 6: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Magnetomotive Force (MMF)

The current flowing in the electrical circuit due to the existence of electromotiveforce(emf) across the circuit

To drive magnetic flux through magnetic circuit, a magneto motive force (mmf)is necessary.

Magnetomotive force can be produced when current flows in a coil of one ormore turns.

The magnitude of mmf is directly proportional to the current I and number ofturns of the coil N,mmf = NI

If the magnetic circuit of magnetic material is homogeneous and of uniformcross sectional area, the magnetomotive force per meter length of the magneticcircuit (path of magnetic flux) is called the magnetic field strength (H).

H =mmf

l

Page 7: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Magnetomotive Force (MMF)

The current flowing in the electrical circuit due to the existence of electromotiveforce(emf) across the circuit

To drive magnetic flux through magnetic circuit, a magneto motive force (mmf)is necessary.

Magnetomotive force can be produced when current flows in a coil of one ormore turns.

The magnitude of mmf is directly proportional to the current I and number ofturns of the coil N,

mmf = NI

If the magnetic circuit of magnetic material is homogeneous and of uniformcross sectional area, the magnetomotive force per meter length of the magneticcircuit (path of magnetic flux) is called the magnetic field strength (H).

H =mmf

l

Page 8: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Magnetomotive Force (MMF)

The current flowing in the electrical circuit due to the existence of electromotiveforce(emf) across the circuit

To drive magnetic flux through magnetic circuit, a magneto motive force (mmf)is necessary.

Magnetomotive force can be produced when current flows in a coil of one ormore turns.

The magnitude of mmf is directly proportional to the current I and number ofturns of the coil N,mmf = NI

If the magnetic circuit of magnetic material is homogeneous and of uniformcross sectional area, the magnetomotive force per meter length of the magneticcircuit (path of magnetic flux) is called the magnetic field strength (H).

H =mmf

l

Page 9: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Magnetomotive Force (MMF)

The current flowing in the electrical circuit due to the existence of electromotiveforce(emf) across the circuit

To drive magnetic flux through magnetic circuit, a magneto motive force (mmf)is necessary.

Magnetomotive force can be produced when current flows in a coil of one ormore turns.

The magnitude of mmf is directly proportional to the current I and number ofturns of the coil N,mmf = NI

If the magnetic circuit of magnetic material is homogeneous and of uniformcross sectional area, the magnetomotive force per meter length of the magneticcircuit (path of magnetic flux) is called the magnetic field strength (H).

H =mmf

l

Page 10: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Magnetomotive Force (MMF)

The current flowing in the electrical circuit due to the existence of electromotiveforce(emf) across the circuit

To drive magnetic flux through magnetic circuit, a magneto motive force (mmf)is necessary.

Magnetomotive force can be produced when current flows in a coil of one ormore turns.

The magnitude of mmf is directly proportional to the current I and number ofturns of the coil N,mmf = NI

If the magnetic circuit of magnetic material is homogeneous and of uniformcross sectional area, the magnetomotive force per meter length of the magneticcircuit (path of magnetic flux) is called the magnetic field strength (H).

H =mmf

l

Page 11: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Reluctance

I

Let the ring have a mean circumference ofl meter, a cross-sectional area of a m2 andN turns carrying a current of I ampere,then the total flux flowing in the dottedpath is given by,

φ = flux density× cross sectional area

φ = B×a

Also, mmf = magnetic field strength×length of flux pathmmf = Hl

Taking ratio of φ and mmf,φ

mmf=

BaHl

But,BH

= µ = µ0µr

φ

mmf= µ0µr

al

ormmf

φ=

lµ0µra

For the electric circuits,emf

current= R =

ρla

As emf/current is called resistance inelectric circuits, mmf/flux can be termedas reluctance for magnetic circuits.

Reluctance is the property of magneticmaterial which opposes the flow of fluxthrough it.

Reluctance R =l

µ0µraampere/weber

Page 12: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Reluctance

I

Let the ring have a mean circumference ofl meter, a cross-sectional area of a m2 andN turns carrying a current of I ampere,then the total flux flowing in the dottedpath is given by,

φ = flux density× cross sectional area

φ = B×a

Also, mmf = magnetic field strength×length of flux pathmmf = Hl

Taking ratio of φ and mmf,φ

mmf=

BaHl

But,BH

= µ = µ0µr

φ

mmf= µ0µr

al

ormmf

φ=

lµ0µra

For the electric circuits,emf

current= R =

ρla

As emf/current is called resistance inelectric circuits, mmf/flux can be termedas reluctance for magnetic circuits.

Reluctance is the property of magneticmaterial which opposes the flow of fluxthrough it.

Reluctance R =l

µ0µraampere/weber

Page 13: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Reluctance

I

Let the ring have a mean circumference ofl meter, a cross-sectional area of a m2 andN turns carrying a current of I ampere,then the total flux flowing in the dottedpath is given by,

φ = flux density× cross sectional area

φ = B×a

Also, mmf = magnetic field strength×length of flux pathmmf = Hl

Taking ratio of φ and mmf,φ

mmf=

BaHl

But,BH

= µ = µ0µr

φ

mmf= µ0µr

al

ormmf

φ=

lµ0µra

For the electric circuits,emf

current= R =

ρla

As emf/current is called resistance inelectric circuits, mmf/flux can be termedas reluctance for magnetic circuits.

Reluctance is the property of magneticmaterial which opposes the flow of fluxthrough it.

Reluctance R =l

µ0µraampere/weber

Page 14: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Reluctance

I

Let the ring have a mean circumference ofl meter, a cross-sectional area of a m2 andN turns carrying a current of I ampere,then the total flux flowing in the dottedpath is given by,

φ = flux density× cross sectional area

φ = B×a

Also, mmf = magnetic field strength×length of flux pathmmf = Hl

Taking ratio of φ and mmf,φ

mmf=

BaHl

But,BH

= µ = µ0µr

φ

mmf= µ0µr

al

ormmf

φ=

lµ0µra

For the electric circuits,emf

current= R =

ρla

As emf/current is called resistance inelectric circuits, mmf/flux can be termedas reluctance for magnetic circuits.

Reluctance is the property of magneticmaterial which opposes the flow of fluxthrough it.

Reluctance R =l

µ0µraampere/weber

Page 15: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Reluctance

I

Let the ring have a mean circumference ofl meter, a cross-sectional area of a m2 andN turns carrying a current of I ampere,then the total flux flowing in the dottedpath is given by,

φ = flux density× cross sectional area

φ = B×a

Also, mmf = magnetic field strength×length of flux pathmmf = Hl

Taking ratio of φ and mmf,φ

mmf=

BaHl

But,BH

= µ = µ0µr

φ

mmf= µ0µr

al

ormmf

φ=

lµ0µra

For the electric circuits,emf

current= R =

ρla

As emf/current is called resistance inelectric circuits, mmf/flux can be termedas reluctance for magnetic circuits.

Reluctance is the property of magneticmaterial which opposes the flow of fluxthrough it.

Reluctance R =l

µ0µraampere/weber

Page 16: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Reluctance

I

Let the ring have a mean circumference ofl meter, a cross-sectional area of a m2 andN turns carrying a current of I ampere,then the total flux flowing in the dottedpath is given by,

φ = flux density× cross sectional area

φ = B×a

Also, mmf = magnetic field strength×length of flux pathmmf = Hl

Taking ratio of φ and mmf,φ

mmf=

BaHl

But,BH

= µ = µ0µr

φ

mmf= µ0µr

al

ormmf

φ=

lµ0µra

For the electric circuits,emf

current= R =

ρla

As emf/current is called resistance inelectric circuits, mmf/flux can be termedas reluctance for magnetic circuits.

Reluctance is the property of magneticmaterial which opposes the flow of fluxthrough it.

Reluctance R =l

µ0µraampere/weber

Page 17: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Reluctance

I

Let the ring have a mean circumference ofl meter, a cross-sectional area of a m2 andN turns carrying a current of I ampere,then the total flux flowing in the dottedpath is given by,

φ = flux density× cross sectional area

φ = B×a

Also, mmf = magnetic field strength×length of flux pathmmf = Hl

Taking ratio of φ and mmf,φ

mmf=

BaHl

But,BH

= µ = µ0µr

φ

mmf= µ0µr

al

ormmf

φ=

lµ0µra

For the electric circuits,emf

current= R =

ρla

As emf/current is called resistance inelectric circuits, mmf/flux can be termedas reluctance for magnetic circuits.

Reluctance is the property of magneticmaterial which opposes the flow of fluxthrough it.

Reluctance R =l

µ0µraampere/weber

Page 18: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Reluctance

I

Let the ring have a mean circumference ofl meter, a cross-sectional area of a m2 andN turns carrying a current of I ampere,then the total flux flowing in the dottedpath is given by,

φ = flux density× cross sectional area

φ = B×a

Also, mmf = magnetic field strength×length of flux pathmmf = Hl

Taking ratio of φ and mmf,φ

mmf=

BaHl

But,BH

= µ = µ0µr

φ

mmf= µ0µr

al

ormmf

φ=

lµ0µra

For the electric circuits,emf

current= R =

ρla

As emf/current is called resistance inelectric circuits, mmf/flux can be termedas reluctance for magnetic circuits.

Reluctance is the property of magneticmaterial which opposes the flow of fluxthrough it.

Reluctance R =l

µ0µraampere/weber

Page 19: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Reluctance

I

Let the ring have a mean circumference ofl meter, a cross-sectional area of a m2 andN turns carrying a current of I ampere,then the total flux flowing in the dottedpath is given by,

φ = flux density× cross sectional area

φ = B×a

Also, mmf = magnetic field strength×length of flux pathmmf = Hl

Taking ratio of φ and mmf,φ

mmf=

BaHl

But,BH

= µ = µ0µr

φ

mmf= µ0µr

al

ormmf

φ=

lµ0µra

For the electric circuits,emf

current= R =

ρla

As emf/current is called resistance inelectric circuits, mmf/flux can be termedas reluctance for magnetic circuits.

Reluctance is the property of magneticmaterial which opposes the flow of fluxthrough it.

Reluctance R =l

µ0µraampere/weber

Page 20: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Reluctance

I

Let the ring have a mean circumference ofl meter, a cross-sectional area of a m2 andN turns carrying a current of I ampere,then the total flux flowing in the dottedpath is given by,

φ = flux density× cross sectional area

φ = B×a

Also, mmf = magnetic field strength×length of flux pathmmf = Hl

Taking ratio of φ and mmf,φ

mmf=

BaHl

But,BH

= µ = µ0µr

φ

mmf= µ0µr

al

ormmf

φ=

lµ0µra

For the electric circuits,emf

current= R =

ρla

As emf/current is called resistance inelectric circuits, mmf/flux can be termedas reluctance for magnetic circuits.

Reluctance is the property of magneticmaterial which opposes the flow of fluxthrough it.

Reluctance R =l

µ0µraampere/weber

Page 21: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Reluctance

I

Let the ring have a mean circumference ofl meter, a cross-sectional area of a m2 andN turns carrying a current of I ampere,then the total flux flowing in the dottedpath is given by,

φ = flux density× cross sectional area

φ = B×a

Also, mmf = magnetic field strength×length of flux pathmmf = Hl

Taking ratio of φ and mmf,φ

mmf=

BaHl

But,BH

= µ = µ0µr

φ

mmf= µ0µr

al

ormmf

φ=

lµ0µra

For the electric circuits,emf

current= R =

ρla

As emf/current is called resistance inelectric circuits, mmf/flux can be termedas reluctance for magnetic circuits.

Reluctance is the property of magneticmaterial which opposes the flow of fluxthrough it.

Reluctance R =l

µ0µraampere/weber

Page 22: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Laws of Magnetic Circuits

Ohm’s law for electric circuit is,emf = current× resistance or E = I ×R

Ohm’s law for magnetic circuit is,mmf = flux× reluctance or mmf = φ ×S

For electric circuits, Resistance =1

conductivity× length

area= ρ

la

For magnetic circuits, Reluctance =1

permeability× length

area=

1µ0µr

× la

In series electric circuits, the total resistance of the circuit is equal to the sum of all theresistance in series.

Similarly, when the flux has to permeate a number of portions of a magnetic circuit inseries, the total reluctance of the complete magnetic circuit will be equal to the sum of thereluctances of various portions, i.e. S = S1 +S2 +S3 + · · ·

Page 23: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Laws of Magnetic Circuits

Ohm’s law for electric circuit is,emf = current× resistance or E = I ×R

Ohm’s law for magnetic circuit is,mmf = flux× reluctance or mmf = φ ×S

For electric circuits, Resistance =1

conductivity× length

area= ρ

la

For magnetic circuits, Reluctance =1

permeability× length

area=

1µ0µr

× la

In series electric circuits, the total resistance of the circuit is equal to the sum of all theresistance in series.

Similarly, when the flux has to permeate a number of portions of a magnetic circuit inseries, the total reluctance of the complete magnetic circuit will be equal to the sum of thereluctances of various portions, i.e. S = S1 +S2 +S3 + · · ·

Page 24: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Laws of Magnetic Circuits

Ohm’s law for electric circuit is,emf = current× resistance or E = I ×R

Ohm’s law for magnetic circuit is,mmf = flux× reluctance or mmf = φ ×S

For electric circuits, Resistance =1

conductivity× length

area= ρ

la

For magnetic circuits, Reluctance =1

permeability× length

area=

1µ0µr

× la

In series electric circuits, the total resistance of the circuit is equal to the sum of all theresistance in series.

Similarly, when the flux has to permeate a number of portions of a magnetic circuit inseries, the total reluctance of the complete magnetic circuit will be equal to the sum of thereluctances of various portions, i.e. S = S1 +S2 +S3 + · · ·

Page 25: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Laws of Magnetic Circuits

Ohm’s law for electric circuit is,emf = current× resistance or E = I ×R

Ohm’s law for magnetic circuit is,mmf = flux× reluctance or mmf = φ ×S

For electric circuits, Resistance =1

conductivity× length

area= ρ

la

For magnetic circuits, Reluctance =1

permeability× length

area=

1µ0µr

× la

In series electric circuits, the total resistance of the circuit is equal to the sum of all theresistance in series.

Similarly, when the flux has to permeate a number of portions of a magnetic circuit inseries, the total reluctance of the complete magnetic circuit will be equal to the sum of thereluctances of various portions, i.e. S = S1 +S2 +S3 + · · ·

Page 26: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Laws of Magnetic Circuits

In a series electric circuit the total voltage drop is equal to the sum of thevoltage drop in various elements of the circuit.

The total mmf required to establish a given flux in the magnetic circuit is equalto the sum of the mmfs necessary to establish the flux through the various partsof the circuit. Thus total mmf of the complete magnetic circuit consisting of anumber of homogeneous parts is given by,

Total mmf F = F1 +F2 +F3 + · · ·

Total mmf F = H1l1 +H2l2 +H3l3 + · · ·

Total mmf F =B1

µ1l1 +

B2

µ2l2 +

B3

µ3l3 + · · ·

The, mmf acting around a complete magnetic circuit is equal to the total ampereturns required to force the given flux through the magnetic circuit.

Page 27: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Laws of Magnetic Circuits

In a series electric circuit the total voltage drop is equal to the sum of thevoltage drop in various elements of the circuit.

The total mmf required to establish a given flux in the magnetic circuit is equalto the sum of the mmfs necessary to establish the flux through the various partsof the circuit. Thus total mmf of the complete magnetic circuit consisting of anumber of homogeneous parts is given by,

Total mmf F = F1 +F2 +F3 + · · ·

Total mmf F = H1l1 +H2l2 +H3l3 + · · ·

Total mmf F =B1

µ1l1 +

B2

µ2l2 +

B3

µ3l3 + · · ·

The, mmf acting around a complete magnetic circuit is equal to the total ampereturns required to force the given flux through the magnetic circuit.

Page 28: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Laws of Magnetic Circuits

In a series electric circuit the total voltage drop is equal to the sum of thevoltage drop in various elements of the circuit.

The total mmf required to establish a given flux in the magnetic circuit is equalto the sum of the mmfs necessary to establish the flux through the various partsof the circuit. Thus total mmf of the complete magnetic circuit consisting of anumber of homogeneous parts is given by,

Total mmf F = F1 +F2 +F3 + · · ·

Total mmf F = H1l1 +H2l2 +H3l3 + · · ·

Total mmf F =B1

µ1l1 +

B2

µ2l2 +

B3

µ3l3 + · · ·

The, mmf acting around a complete magnetic circuit is equal to the total ampereturns required to force the given flux through the magnetic circuit.

Page 29: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Laws of Magnetic Circuits

In a series electric circuit the total voltage drop is equal to the sum of thevoltage drop in various elements of the circuit.

The total mmf required to establish a given flux in the magnetic circuit is equalto the sum of the mmfs necessary to establish the flux through the various partsof the circuit. Thus total mmf of the complete magnetic circuit consisting of anumber of homogeneous parts is given by,

Total mmf F = F1 +F2 +F3 + · · ·

Total mmf F = H1l1 +H2l2 +H3l3 + · · ·

Total mmf F =B1

µ1l1 +

B2

µ2l2 +

B3

µ3l3 + · · ·

The, mmf acting around a complete magnetic circuit is equal to the total ampereturns required to force the given flux through the magnetic circuit.

Page 30: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Comparison between the Electric and Magnetic Circuit

Similarities in Electric and Magnetic Circuit

Current flows in the circuit. Flux is assumed to flowThe path of current is called electric circuit Path of flux is called magnetic circuit.Current flows due to emf Flux flows due to mmfFlow of current is restricted by resistance ofthe circuit

Flow of flux is restricted by reluctance ofthe circuit

Current = emf/Resistance Flux = mmf/reluctance

R = ρla

S =l

µA

Dissimilarities in Electrical and Magnetic circuit

Current is actually flows in the circuit. Flux does not flow, it is only assumed toflow for finding out certain magnetic ef-fects.

Energy is needed till the current flows. Energy is needed only to create the mag-netic flux

Resistance of the circuit is independent ofthe current.

Reluctance of the circuit changes with themagnetic flux

Page 31: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Comparison between the Electric and Magnetic Circuit

Similarities in Electric and Magnetic Circuit

Current flows in the circuit. Flux is assumed to flowThe path of current is called electric circuit Path of flux is called magnetic circuit.Current flows due to emf Flux flows due to mmfFlow of current is restricted by resistance ofthe circuit

Flow of flux is restricted by reluctance ofthe circuit

Current = emf/Resistance Flux = mmf/reluctance

R = ρla

S =l

µA

Dissimilarities in Electrical and Magnetic circuit

Current is actually flows in the circuit. Flux does not flow, it is only assumed toflow for finding out certain magnetic ef-fects.

Energy is needed till the current flows. Energy is needed only to create the mag-netic flux

Resistance of the circuit is independent ofthe current.

Reluctance of the circuit changes with themagnetic flux

Page 32: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Calculation of Ampere Turns for the Air Gap

Total ampere turns for the air gap is given by,

ATg = flux× reluctance

ATg = φ ×lg

µ0Ag

ATg =φ

Ag

lgµ0

ATg = Bg ×1µ0

lg

ATg =1

4π ×10−7 Bglg

ATg = 0.796Bglg ×106

Page 33: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Example 1

The magnetic frame shown in figure is built up of iron of square cross-section, 3 cmside. Each air gap is 2 mm wide. Each of the coil is wound with 1000 turns and theexciting current is 1.0 A. The relative permeability of Part A and Part B may be takenas 1000 and 1200 respectively. Calculate the following. (i) reluctance of part A (ii)reluctance of part B (iii) reluctance of two air gaps (iv) total reluctance of completemagnetic circuit (v) the mmf (vi) total flux (vii)flux density.

Part A

Part B

17 cm

20 cm

2 mm

10 cm

Page 34: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Example 1

The magnetic frame shown in figure is built up of iron of square cross-section, 3 cmside. Each air gap is 2 mm wide. Each of the coil is wound with 1000 turns and theexciting current is 1.0 A. The relative permeability of Part A and Part B may be takenas 1000 and 1200 respectively. Calculate the following. (i) reluctance of part A (ii)reluctance of part B (iii) reluctance of two air gaps (iv) total reluctance of completemagnetic circuit (v) the mmf (vi) total flux (vii)flux density.

Part A

Part B

17 cm

20 cm

2 mm

10 cm

Page 35: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Example 1

Reluctance for part A, SA =lA

µ0µraCross sectional area of partA = 0.03×0.03 = 9×10−4m2

SA =0.17

4π ×10−7 ×1000×9×10−4

SA = 15.03×104AT/wb

Reluctance of part B, SB =lb

µ0µraLength of part B,lb = 17+8.5+8.5 = 34cm = 0.34m

SB =0.34

4π ×10−7 ×1000×9×10−4

SB = 25.04×104AT/wb

Reluctance of air gap, Sg =lg

µ0aLength of air gap is 2+2=4mm

Sg =4×10−3

4π ×10−7 ×9×10−4

Sg = 353.5×104AT/wb

Total Reluctance S = SA +SB +Sg

S = (15.03+25.04+353.5)×104

S = 393.57×104AT/wb

mmf = 2×1000×1.0 = 2000AT

flux =mmf

reluctance=

2000393.57×104

flux = 5.08×10−4wb

Flux Density =flux

cross sectional area

B =5.08×10−4

9×10−4 = 0.564Wb/m2

Page 36: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Example 2

A cast steel electromagnet has an air gap length of 3 mm and an iron path of length40 cm. Find the number of ampere turn necessary to produced a flux density of 0.7wb/m2 in the gap.

Ampere turns for the air gap is given by,

ATg = 0.796Bglg ×106

ATg = 0.796×0.7×0.4×106

ATg = 1671AT

Page 37: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Example 2

A cast steel electromagnet has an air gap length of 3 mm and an iron path of length40 cm. Find the number of ampere turn necessary to produced a flux density of 0.7wb/m2 in the gap.

Ampere turns for the air gap is given by,

ATg = 0.796Bglg ×106

ATg = 0.796×0.7×0.4×106

ATg = 1671AT

Page 38: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Example 2

A cast steel electromagnet has an air gap length of 3 mm and an iron path of length40 cm. Find the number of ampere turn necessary to produced a flux density of 0.7wb/m2 in the gap.

Ampere turns for the air gap is given by,

ATg = 0.796Bglg ×106

ATg = 0.796×0.7×0.4×106

ATg = 1671AT

Page 39: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Example 2

A cast steel electromagnet has an air gap length of 3 mm and an iron path of length40 cm. Find the number of ampere turn necessary to produced a flux density of 0.7wb/m2 in the gap.

Ampere turns for the air gap is given by,

ATg = 0.796Bglg ×106

ATg = 0.796×0.7×0.4×106

ATg = 1671AT

Page 40: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Example 2

A cast steel electromagnet has an air gap length of 3 mm and an iron path of length40 cm. Find the number of ampere turn necessary to produced a flux density of 0.7wb/m2 in the gap.

Ampere turns for the air gap is given by,

ATg = 0.796Bglg ×106

ATg = 0.796×0.7×0.4×106

ATg = 1671AT

Page 41: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Example 3

A steel ring of 25 cm mean diameter and of circular section 3 cm in diameter has anair gap of 1.5 mm length. It wound uniformly with 700 turns of wire carrying acurrent of 2A. Calculate (i) magnetomotive force (ii) flux density (iii)magnetic flux(iv) reluctance (v) relative permeability of steel ring. Neglect magnetic leakage andassume that the iron path takes about 35 percent of total megnetomotive force.

Calculation Magnetomotive forcemmf = total turns × currentmmf = 700×2mmf = 1400 AT

Calculation of flux densityTotal AT = 1400Iron part takes about 35% of total mmf, thus airpart takes 65% of total mmfATg = 0.65×1400ATg = 910910 = 0.796×Bglg ×106

Bg =910

0.796×1.5×10−3 ×106 = 0.762 wb/m2

Calculation of flux φ

φ = B×Aφ = 0.762×π ×0.0152 = 0.538 mWb

Calculation of ReluctanceReluctance =

mmfφ

Reluctance =1400

0.538m = 2.6×106 AT/wb

Calculation of µr for steel ring,mmf for steel ring is 0.35 x 1400 = 490

mmf = Hl =B

µ0µrl

µr =Bl

mmf ×µ0=

0.762×π ×0.25490×4π ×10−7

µr = 971.9

Page 42: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Example 3

A steel ring of 25 cm mean diameter and of circular section 3 cm in diameter has anair gap of 1.5 mm length. It wound uniformly with 700 turns of wire carrying acurrent of 2A. Calculate (i) magnetomotive force (ii) flux density (iii)magnetic flux(iv) reluctance (v) relative permeability of steel ring. Neglect magnetic leakage andassume that the iron path takes about 35 percent of total megnetomotive force.

Calculation Magnetomotive forcemmf = total turns × currentmmf = 700×2mmf = 1400 AT

Calculation of flux densityTotal AT = 1400Iron part takes about 35% of total mmf, thus airpart takes 65% of total mmfATg = 0.65×1400ATg = 910910 = 0.796×Bglg ×106

Bg =910

0.796×1.5×10−3 ×106 = 0.762 wb/m2

Calculation of flux φ

φ = B×Aφ = 0.762×π ×0.0152 = 0.538 mWb

Calculation of ReluctanceReluctance =

mmfφ

Reluctance =1400

0.538m = 2.6×106 AT/wb

Calculation of µr for steel ring,mmf for steel ring is 0.35 x 1400 = 490

mmf = Hl =B

µ0µrl

µr =Bl

mmf ×µ0=

0.762×π ×0.25490×4π ×10−7

µr = 971.9

Page 43: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Example 4

A total flux of 0.0006 Wb is required in the air gap of an iron ring of cross-section 5.5cm2 and mean length 2.7 m with an air gap of 4.5 mm. Find the number of ampereturns required. Points on the B-H curve for the material of the ring are as follows:

H(AT/m): 200 400 500 600 800 1000B(Wb/m2): 0.4 0.8 1.0 1.09 1.17 1.19

Flux φ = 0.0006 Wb

Flux density B =φ

A=

0.00065.5×10−4 = 1.09Wb/m2

ATg = 0.796×Bglg ×106

ATg = 0.796×1.09×4.5×10−3 ×106

ATg = 3904

Ampere turns calculation for iron ringAT = HlAT = 600× (2.7−4.5×10−3)AT = 1617

Total ampere turns = 3904 + 1617 = 5521

Page 44: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Example 4

A total flux of 0.0006 Wb is required in the air gap of an iron ring of cross-section 5.5cm2 and mean length 2.7 m with an air gap of 4.5 mm. Find the number of ampereturns required. Points on the B-H curve for the material of the ring are as follows:

H(AT/m): 200 400 500 600 800 1000B(Wb/m2): 0.4 0.8 1.0 1.09 1.17 1.19

Flux φ = 0.0006 Wb

Flux density B =φ

A=

0.00065.5×10−4 = 1.09Wb/m2

ATg = 0.796×Bglg ×106

ATg = 0.796×1.09×4.5×10−3 ×106

ATg = 3904

Ampere turns calculation for iron ringAT = HlAT = 600× (2.7−4.5×10−3)AT = 1617

Total ampere turns = 3904 + 1617 = 5521

Page 45: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Leakage Flux and Fringing

The total magnetic flux, φt produced by the coil due to current I flowing in it isdivided into following two components.

1 Useful flux φ , which flows throughout the magnetic circuit and is utilized forthe useful purpose. In case of transformer, the flux which links both the primaryand secondary winding is called useful flux and in case of rotating machines theflux which crosses the air gap is called the useful flux.

2 Leakage flux φl, links partly the magnetic circuit and complete its path throughair as shown in figure. In case of transformer the flux which links with onewinding only and complete its path trough air is called leakage flux. The valueof leakage flux depends on the load current.

Thus, the total flux produced, φt is equal to the sum of the useful flux phi and theleakage flux φl.

φT = φ +φl

Page 46: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Leakage Flux and Fringing

The total magnetic flux, φt produced by the coil due to current I flowing in it isdivided into following two components.

1 Useful flux φ , which flows throughout the magnetic circuit and is utilized forthe useful purpose. In case of transformer, the flux which links both the primaryand secondary winding is called useful flux and in case of rotating machines theflux which crosses the air gap is called the useful flux.

2 Leakage flux φl, links partly the magnetic circuit and complete its path throughair as shown in figure. In case of transformer the flux which links with onewinding only and complete its path trough air is called leakage flux. The valueof leakage flux depends on the load current.

Thus, the total flux produced, φt is equal to the sum of the useful flux phi and theleakage flux φl.

φT = φ +φl

Page 47: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Leakage Flux and Fringing

The total magnetic flux, φt produced by the coil due to current I flowing in it isdivided into following two components.

1 Useful flux φ , which flows throughout the magnetic circuit and is utilized forthe useful purpose. In case of transformer, the flux which links both the primaryand secondary winding is called useful flux and in case of rotating machines theflux which crosses the air gap is called the useful flux.

2 Leakage flux φl, links partly the magnetic circuit and complete its path throughair as shown in figure. In case of transformer the flux which links with onewinding only and complete its path trough air is called leakage flux. The valueof leakage flux depends on the load current.

Thus, the total flux produced, φt is equal to the sum of the useful flux phi and theleakage flux φl.

φT = φ +φl

Page 48: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Leakage Flux and Fringing

The total magnetic flux, φt produced by the coil due to current I flowing in it isdivided into following two components.

1 Useful flux φ , which flows throughout the magnetic circuit and is utilized forthe useful purpose. In case of transformer, the flux which links both the primaryand secondary winding is called useful flux and in case of rotating machines theflux which crosses the air gap is called the useful flux.

2 Leakage flux φl, links partly the magnetic circuit and complete its path throughair as shown in figure. In case of transformer the flux which links with onewinding only and complete its path trough air is called leakage flux. The valueof leakage flux depends on the load current.

Thus, the total flux produced, φt is equal to the sum of the useful flux phi and theleakage flux φl.

φT = φ +φl

Page 49: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Leakage Flux and Fringing

The ratio of the total flux produced φT to the useful flux phi is called the leakagefactor or leakage coefficient, that is,

leakage factor =φT

φ

The value of the leakage factor is always grater than unity and varies between 1.15 to1.25 depending upon the type of magnetic circuit

When the flux crosses the air gap, it tends to bulge out across the edges of the air gap.This effect of bulging is called fringing. The effect of fringing is to increase theeffective gap area, which in turn reduces the flux density in the air gap. Fringingdepends upon the length of the air gap, that is higher the air gap greater is thefringing.

Page 50: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Leakage Flux and Fringing

The ratio of the total flux produced φT to the useful flux phi is called the leakagefactor or leakage coefficient, that is,

leakage factor =φT

φ

The value of the leakage factor is always grater than unity and varies between 1.15 to1.25 depending upon the type of magnetic circuit

When the flux crosses the air gap, it tends to bulge out across the edges of the air gap.This effect of bulging is called fringing. The effect of fringing is to increase theeffective gap area, which in turn reduces the flux density in the air gap. Fringingdepends upon the length of the air gap, that is higher the air gap greater is thefringing.

Page 51: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Leakage Flux and Fringing

The ratio of the total flux produced φT to the useful flux phi is called the leakagefactor or leakage coefficient, that is,

leakage factor =φT

φ

The value of the leakage factor is always grater than unity and varies between 1.15 to1.25 depending upon the type of magnetic circuit

When the flux crosses the air gap, it tends to bulge out across the edges of the air gap.This effect of bulging is called fringing. The effect of fringing is to increase theeffective gap area, which in turn reduces the flux density in the air gap. Fringingdepends upon the length of the air gap, that is higher the air gap greater is thefringing.

Page 52: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Magnetic Hysteresis

If a magnetic material is magnetized in a strong magnetic field, it retains aconsiderable portion of magnetism even after the removal of the magnetic force.This phenomenon of lagging of magnetization of flux density B behind themagnetizing force H is known as magnetic hysteresis.

Residual magnetism or remanent flux density is defined as the magnetic fluxdensity which still remains in magnetic material even when the magnetizingforce is completely removed.

The magnetic field intensity required to wipe out the residual magnetism iscalled coercive force.

Page 53: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Magnetic Hysteresis

If a magnetic material is magnetized in a strong magnetic field, it retains aconsiderable portion of magnetism even after the removal of the magnetic force.This phenomenon of lagging of magnetization of flux density B behind themagnetizing force H is known as magnetic hysteresis.

Residual magnetism or remanent flux density is defined as the magnetic fluxdensity which still remains in magnetic material even when the magnetizingforce is completely removed.

The magnetic field intensity required to wipe out the residual magnetism iscalled coercive force.

Page 54: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Magnetic Hysteresis

If a magnetic material is magnetized in a strong magnetic field, it retains aconsiderable portion of magnetism even after the removal of the magnetic force.This phenomenon of lagging of magnetization of flux density B behind themagnetizing force H is known as magnetic hysteresis.

Residual magnetism or remanent flux density is defined as the magnetic fluxdensity which still remains in magnetic material even when the magnetizingforce is completely removed.

The magnetic field intensity required to wipe out the residual magnetism iscalled coercive force.

Page 55: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Magnetic Hysteresis

If a magnetic material is magnetized in a strong magnetic field, it retains aconsiderable portion of magnetism even after the removal of the magnetic force.This phenomenon of lagging of magnetization of flux density B behind themagnetizing force H is known as magnetic hysteresis.

Residual magnetism or remanent flux density is defined as the magnetic fluxdensity which still remains in magnetic material even when the magnetizingforce is completely removed.

The magnetic field intensity required to wipe out the residual magnetism iscalled coercive force.

Page 56: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Magnetic Hysteresis

If a magnetic material is magnetized in a strong magnetic field, it retains aconsiderable portion of magnetism even after the removal of the magnetic force.This phenomenon of lagging of magnetization of flux density B behind themagnetizing force H is known as magnetic hysteresis.

Residual magnetism or remanent flux density is defined as the magnetic fluxdensity which still remains in magnetic material even when the magnetizingforce is completely removed.

The magnetic field intensity required to wipe out the residual magnetism iscalled coercive force.

Page 57: Magnetic Circuit

Magnetomotive Force (MMF) Reluctance

Magnetic Hysteresis

Retentivity is the power of retaining magnetism in the magnetic materials even after themagnetizing force is completely removed.

Coercive force is the demagnetizing force which is necessary to neutralize completely themagnetism in the magnetic material.

The shape of the hysteresis loop will depend upon the nature of magnetic material.

Hysteresis loop for hard steel is quite wide and hence possess high retentivity power andlarge coercive force. This type of material is well suited for permanent magnets and notsuitable for rapid reversals of magnetization as in transformer core and choke cores.

Steel, silicon alloys have a very narrow hysteresis loop. Since they have very highpermeability and very low hysteresis losses, these materials are more suitable fortransformer core and armature cores which are subjected to rapid reversal ofmagnetization.

When a magnetic material is subjected to cyclic changes of magnetization, the domainschanges the direction of their orientation according to the way the applied magnetizingforce H changes its direction. Work is done in changing the direction of the domainswhich leads to the production of heat within the material. The energy required in takingthe material through one complete cycle of magnetization is proportional to the areaenclosed by the hysteresis loop.

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Magnetomotive Force (MMF) Reluctance

Hysteresis loss

If the magnetization is carried through a complete cycle, the energy wasted isproportional to the area of the hysteresis loop and the shape of hysteresis loopdepends upon the nature of the ferromagnetic material.

Hysteresis loss is equal to the energy consumed in magnetizing anddemagnetizing a magnetic material .

It is proportional to ,

Area enclosed in the hysteresis loop

Frequency of magnetic flux reversal

Volume of the magnetic material

Hysteresis loss, Ph = ηVf (Bmax)1.6

V = Volume of material in m3

η is a constant, steinmetz’s coefficient

f is frequency of magnetic flux reversal

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Magnetomotive Force (MMF) Reluctance

Eddy Currents

When a magnetic material is linked with a variable or alternating flux, an emf isinduced in the magnetic material itself according to Faraday’s law ofelectromagnetic induction. This induced emf circulates a current in the body ofthe magnetic material. These circulating currents are called Eddy currents andpower losses due to the flow of this current are called Eddy current losses.

Eddy currents always tend to flow in planes perpendicular to the magnetic fluxas they are induced due to variation of this flux through the circuit.

Applications of eddy current include eddy current braking in induction energymeters and eddy current damping in permanent magnet moving coilinstruments.

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Magnetomotive Force (MMF) Reluctance

Eddy current loss

Power loss due to flow of eddy currents in the magnetic material is called Eddycurrent loss. Heat is generated due to flow of eddy current. Basically, eddy currentloss depends upon the value of the emf induced and the resistance offered by themagnetic material to the flow of eddy currents. The resistance can greatly increasedby laminating the material, thereby reducing the magnitude of the eddy currents to anappreciable value.

The eddy current losses depends upon the following things,

1 Thickness of the material2 Frequency of flux reversal3 Maximum value of flux density4 Volume of the material5 Quality of material

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Magnetomotive Force (MMF) Reluctance

Classification of Magnetic Materials

1 Ferromagnetic MaterialsThe materials whose relative permeability is very high (µr =100 to 10000) arecalled the ferromagnetic materials, e.g. iron, steel, nickel, cobalt etc. Suchmaterials can be used to make strong magnets as they are strongly attracted bymagnets.

2 Paramagnetic MaterialsThe materials having relative permeability equal to one or slightly more thanone are called the paramagnetic materials. e.g. platinum, manganese, aluminumetc. These materials are attracted by a magnet but not very strongly.

3 Diamagnetic MaterialsThe materials having their relative permeability less than one are called thediamagnetic materials, e.g. zinc, bismuth, sulfur, phosphorous, tin, lead etc.Such materials are actually repelled by a magnet.

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Magnetomotive Force (MMF) Reluctance

Classification of Magnetic Materials

1 Ferromagnetic MaterialsThe materials whose relative permeability is very high (µr =100 to 10000) arecalled the ferromagnetic materials, e.g. iron, steel, nickel, cobalt etc. Suchmaterials can be used to make strong magnets as they are strongly attracted bymagnets.

2 Paramagnetic MaterialsThe materials having relative permeability equal to one or slightly more thanone are called the paramagnetic materials. e.g. platinum, manganese, aluminumetc. These materials are attracted by a magnet but not very strongly.

3 Diamagnetic MaterialsThe materials having their relative permeability less than one are called thediamagnetic materials, e.g. zinc, bismuth, sulfur, phosphorous, tin, lead etc.Such materials are actually repelled by a magnet.

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Magnetomotive Force (MMF) Reluctance

Classification of Magnetic Materials

1 Ferromagnetic MaterialsThe materials whose relative permeability is very high (µr =100 to 10000) arecalled the ferromagnetic materials, e.g. iron, steel, nickel, cobalt etc. Suchmaterials can be used to make strong magnets as they are strongly attracted bymagnets.

2 Paramagnetic MaterialsThe materials having relative permeability equal to one or slightly more thanone are called the paramagnetic materials. e.g. platinum, manganese, aluminumetc. These materials are attracted by a magnet but not very strongly.

3 Diamagnetic MaterialsThe materials having their relative permeability less than one are called thediamagnetic materials, e.g. zinc, bismuth, sulfur, phosphorous, tin, lead etc.Such materials are actually repelled by a magnet.